The growth of mid-wavelength infrared InAs/GaSb superlattice on GaSb substrates by molecular beam epitaxy (MBE)was studied. We optimized the substrate temperature and interface structures to obtain high quality material. The InAs/GaSb superlattice layers were characterized by Atomic Force Microscope(AFM), high resolution X-ray diffraction (XRD) and Fourier Transform Infrared Spectrum. We found the optimal substrate temperature for GaSb and superlattice is 485℃ and 450℃ respectively. We finally obtained highly lattice matched InAs/GaSb materials with 50% cut-off wavelength at 4.84 μm at 77 K.